Question: Let matrix A R n x n . (a) Please explain how to prove that if is an eigenvalue of A , then 2 is

Let matrix ARnxn .

(a) Please explain how to prove that if is an eigenvalue of A, then 2 is an eigenvalue of A2 .

(b) Please show how to prove that if A is invertible, then A2 is positive-definite.

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